We consider the infiltration of a wetting fluid into a homogeneous porous medium and the formation of preferential flow paths with saturation overshoots. These are caused by dynamic capillary pressure effects which can be modeled by the rate-dependent approach of Hassanizadeh and Gray. To track the overshoot wave numerically, we propose an extended Heterogeneous Multiscale Method. In the approach, the rate-dependent model takes the role of a microscale model. The algorithm is applied to several infiltration problems.

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